SMS scnews item created by Uri Keich at Fri 30 Jul 2010 0308
Type: Seminar
Distribution: World
Expiry: 6 Aug 2010
Calendar1: 6 Aug 2010 1400-1500
CalLoc1: Carslaw 173
Auth: uri@cpe-144-131-104-252.lns2.cht.bigpond.net.au (ukeich) in SMS-WASM

# Statistics Seminar: Philip Kokic -- Multivariate quantiles, expectiles and M-quantiles

Philip Kokic Mathematics, Informatics and Statistics CSIRO

Location: Carslaw 173

Time: 2pm Friday, August 6, 2010

Title: Multivariate quantiles, expectiles and M-quantiles

Abstract: Ordinary quantiles and expectiles are special cases of univariate M-quantiles,
which can be defined either in terms of the minimum of a specific loss function or the
solution to the corresponding estimating equation.  In this presentation we show how
M-quantiles can be extended to a multivariate situation by generalising the estimating
equation approach.  Some of the features and properties of Multivariate M-quantiles are
explored using a variety of simulated data sets.  In particular, it is illustrated how,
to a certain extent, they are able to capture non-linear relationships between
variables.  For data of more than 1 dimension they are unique and can also be computed
efficiently even for high dimensional data.  Unlike alternatives based on multivariate
density estimates they do not suffer from ’the curse of dimensionality’.

Multivariate outliers present some interesting statistical issues; for example, an
outlier may or may not become an influential observation depending on the type of
analysis performed.  In this presentation we also describe how M-quantiles need to be
modified for multivariate outlier detection.  To this end a semi-parametric form of
multivariate expectiles is described, and the approach is illustrated using UK annual